Cartons or boxes are often used for storing and merchandising consumer goods. Such cartons may be formed from flat paperboard blanks, which are folded, filled with product, and sealed by machines in an automated process. Depending upon the configuration of the panels and flaps of the blank which fold together to form the carton, the number of blanks that can fit on a single sheet of material may be limited. In addition, the portions of the sheet of material that remain as wasted blank pieces after the blanks are removed (e.g., cut out) may take up a significant part of the sheet of material. Conventionally, these wasted portions of the sheet of material that remain after removing the blanks for the individual cartons are substantial. In some cases, as much as 55% of a flat blank goes wasted as the cutout portions. Conventional packaging systems used by consumer packaged-goods companies have not been entirely successful in lowering the environmental impact of the packages they use to package, distribute and market their products at retail, while increasing packaging productivity across the supply chain.